Eeek! Ants on the Clock

Posted May 20 - 26, 1996

Ant #1 is sitting on the edge of the hour hand on a circular clock. Ant#2 is sitting on edge of the minute hand on the same clock. How many times per day do Ant#1 and Ant #2 meet up?Ant #1 and Ant#2 begin by meeting up at 12:00 a.m.

They next meet up between 1:05 a.m. and 1:09 a.m.

They next meet up between 2:10 a.m. and 2:14 a.m.

They next meet up between 3:15 a.m. and 3:19 a.m.

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The ants meet up at 12:00 p.m.

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The ants meet up for the final time that day between 11:55 and 11:59 p.m.The ants will meet up 24 times in a 24-hour day.

Peter Letts [pjletts@ottawa.net] gave Minus a solution that had the right idea, but his day included an extra 1 second (i.e. 24 hours + 1 second):

The ants on the clock will meet up 25 times a day. Every hour the two hands pass each other, therefore they will meet up 24 times. The twenty fifth is at midnight at the end of the day, when the hands are on top of each other.Debbie Neuhaus [neuhaus@planet.net] didn't include an explanation, but she was correct:

24 times a day.

the only correct answers for this fairly

straight-forward question.

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Thanks to everyone who submitted solutions.
Keep up the great work!*